CAT 2026 · Slot 2 · Expected paper

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CAT 2026 Slot 2 DILR Q2: CAT DILR set

The set
SET 1: CURRENCY AND TRAVEL COSTS
Yuronia, Velsoria, Kytheria and Xandoria use Yurons, Velins, Kythens and Xentars respectively. 1 Kythen = 0.5 Xentars. Three travelers—Rohan, Nisha and Tanya—start from Xandoria and each visits exactly two countries. Each of the three destination countries is visited by exactly two travelers. Each traveler's flight cost (including both onward flights and the return flight) is unique. Rohan's flight cost is 4000 Xentars; the other two flight costs are 5000 and 6000 Xentars, in an unknown order. On each visit, a traveler spends either 1000, 2000 or 3000 units of the local currency. Each traveler's two spends are different. Across all six visits, there are exactly two spends of 1000 and exactly one spend of 3000. Travel Cost = Flight Cost + the Xentar equivalent of the two local-currency spends.
OBSERVATIONS:
(i) Yuronia: Rohan and Nisha visited. Their Travel Costs were 3500 and 8000 Yurons respectively.
(ii) Velsoria: Nisha and Tanya visited, spending 2000 and 3000 Velins respectively. Nisha's Travel Cost was 4000 Velins.
(iii) Kytheria: Tanya visited and her Travel Cost was 36000 Kythens.
Use the observations in the local currency of the country making each observation.

TITA (type the answer) · +3 / 0 · medium

How many Xentars did Tanya spend in the two countries she visited?
Answer and solution

Correct answer: 13000

Solution

Answer: 13000

1. Work in thousands of currency units. Nisha visits Yuronia and Velsoria. Her 2000 Velin spend means her Yuronia spend cannot be 2000; the only 3000 spend is already Tanya's. Thus Nisha spends 1000 Yurons.
2. Nisha's same total cost is 8000 Yurons and 4000 Velins, so one Velin is worth two Yurons. Let one Yuron be y Xentars; then one Velin=2y Xentars.
3. Nisha's spending is 1000y+2000(2y)=5000y and her travel cost is 8000y. Her flight cost is 3000y, hence y is 5/3 or 2 because her flight costs 5000 or 6000.
4. Rohan visits Yuronia and Kytheria. His two spends must be 1000 and 2000 in some order. If Yuronia=1000 and Kytheria=2000, then 3500y=4000+1000y+1000, giving y=2. Reversing the spends gives y=3, incompatible with Nisha. Hence y=2.
5. Therefore Velin=4 Xentars, Nisha flight=6000, Tanya flight=5000. Rohan spends 1000 Yurons and 2000 Kythens. Exactly two 1000 spends are used by Rohan and Nisha, so Tanya spends 2000 Kythens alongside 3000 Velins.
6. Complete check: travel costs are Rohan 7000, Nisha 16000, Tanya 18000 Xentars. Each traveller has different local spend amounts; all six spends have two 1000s, three 2000s and one 3000.
7. Tanya local spending is 3000×4+2000×0.5=13000 Xentars; her total 18000 minus flight 5000 agrees.
8. Answer: 13000 Xentars

G Strategy shortcut

Method: Tanya local spending is 3000×4+2000×0.5=13000 Xentars; her total 18000 minus flight 5000 agrees.
Verification: 1. Work in thousands of currency units. Nisha visits Yuronia and Velsoria. Her 2000 Velin spend means her Yuronia spend cannot be 2000; the only 3000 spend is already Tanya's. Thus Nisha spends 1000 Yurons.
2. Nisha's same total cost is 8000 Yurons and 4000 Velins, so one Velin is worth two Yurons. Let one Yuron be y Xentars; then one Velin=2y Xentars.
3. Nisha's spending is 1000y+2000(2y)=5000y and her travel cost is 8000y. Her flight cost is 3000y, hence y is 5/3 or 2 because her flight costs 5000 or 6000.
4. Rohan visits Yuronia and Kytheria. His two spends must be 1000 and 2000 in some order. If Yuronia=1000 and Kytheria=2000, then 3500y=4000+1000y+1000, giving y=2. Reversing the spends gives y=3, incompatible with Nisha. Hence y=2.
5. Therefore Velin=4 Xentars, Nisha flight=6000, Tanya flight=5000. Rohan spends 1000 Yurons and 2000 Kythens. Exactly two 1000 spends are used by Rohan and Nisha, so Tanya spends 2000 Kythens alongside 3000 Velins.
6. Complete check: travel costs are Rohan 7000, Nisha 16000, Tanya 18000 Xentars. Each traveller has different local spend amounts; all six spends have two 1000s, three 2000s and one 3000.
7. Tanya local spending is 3000×4+2000×0.5=13000 Xentars; her total 18000 minus flight 5000 agrees.
8. Answer: 13000 Xentars

G Strategy: Method: Tanya local spending is 3000×4+2000×0.5=13000 Xentars; her total 18000 minus flight 5000 agrees. Verification: 1. Work in thousands of currency units. Nisha visits Yuronia and Velsoria. Her 2000 Velin spend means her Yuronia spend cannot be 2000; the only 3000 spend is already Tanya's. Thus Nisha spends 1000 Yurons. 2. Nisha's same total cost is 8000 Yurons and 4000 Velins, so one Velin is worth two Yurons. Let one Yuron be y Xentars; then one Velin=2y Xentars. 3. Nisha's spending is 1000y+2000(2y)=5000y and her travel cost is 8000y. Her flight cost is 3000y, hence y is 5/3 or 2 because her flight costs 5000 or 6000. 4. Rohan visits Yuronia and Kytheria. His two spends must be 1000 and 2000 in some order. If Yuronia=1000 and Kytheria=2000, then 3500y=4000+1000y+1000, giving y=2. Reversing the spends gives y=3, incompatible with Nisha. Hence y=2. 5. Therefore Velin=4 Xentars, Nisha flight=6000, Tanya flight=5000. Rohan spends 1000 Yurons and 2000 Kythens. Exactly two 1000 spends are used by Rohan and Nisha, so Tanya spends 2000 Kythens alongside 3000 Velins. 6. Complete check: travel costs are Rohan 7000, Nisha 16000, Tanya 18000 Xentars. Each traveller has different local spend amounts; all six spends have two 1000s, three 2000s and one 3000. 7. Tanya local spending is 3000×4+2000×0.5=13000 Xentars; her total 18000 minus flight 5000 agrees. 8. Answer: 13000 Xentars

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